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Saturday, October 21, 2006

Gambling By Numbers

After much healthy debate regarding how to sensibly speculate as to who will be eliminated from tonight's show prior to hearing a note sung, we have been trying to develop a system that incorporates all the different variables that people feel are important.

We have the basis of such a system, but as always it is only as good as the assumptions that underly it. The assumptions that we are making in this case are as follows:

1. The acts begin the night ranked in terms of public popularity based on their current standing in the polls.

2. Each act has a prior probability of making a hash of their song.

3. Each act has a conditional probability that they find themselves in contention for the bottom two places in terms of number of public votes, assuming that they do make a hash of their song tonight.

4. An act that is less popular in the polls can avoid being in contention for the bottom two placings by not making a hash of their song, if and only if there exists an act more popular than them that does make a hash of their song, under the probabilities defined above.

5. For each possible pairing their is a probability that each act will be eliminated by the judges, given that they make the final two this evening.Using these assumptions, we can run a simulation of what may happen tonight. In fact, we can run thousands of simulations as to what may happen tonight and observe what the relative frequency is of each act ending up getting the boot this evening.

Obviously we have run this model with our own interpretations of the probabilities required as inputs. However, I am reluctant to publish the results of this because it will most likely evoke discussions about our subjective inputs, rather than the effectiveness of the model itself. What I can say is that under our assumptions, the Mcdonald Brothers look like they have got alot of work to do to avoid being in the bottom two this evening.

If any readers would like to suggest inputs for the model, we can look for value in the betting markets accordingly.